Archive for December, 2018

Wikipedia has an accurate biography

Sunday, December 30th, 2018

Wikipedia has an accurate biography

This is found in www.wiki.naturalphilosophy.org and this is an accurate account of my work, a shortened version of my many entries in Marquis Who’s Who. So the lunatic abusers are excommunicate and anathema. ECE has generated tens of millions of readings and is famous throughout the world of science. It is rigorously Baconian science, a correct theory tested hundreds of times by computer, dialogue and experimental data. Much of standard physics is in tatters, it is essentially a refuted pseudoscience with as many parameters as a hedgehog, leading nowhere. No dog(matist) puts his nose in a hedgehog twice. It is well known that B(3) has been nominated for a Nobel Prize several times. There was a disgraceful campaign against my work just after I had been appointed a Civil List Pensioner. Seven hundred papers and books later, that campaign looks like a dog with a bloody nose. The colleagues at AIAS / UPITEC should also have entries in Wikipedia’s Natural Philosophy section. I do not know who posted my entry but this time it has not been interfered with by Lakhtakia or other abusers and pseudoscientists.

Fwd: relativistic Hamilton equations

Sunday, December 30th, 2018

Relativistic Hamilton equations

This is all excellent work, and any method is equally valid mathematically. It will be interesting to see which method is the most computationally efficient, and whether any new information emerges, such as that in UFT425, using a combination of Euler Lagrange and Hamilton. I think that these nineteenth century methods can be made considerably more powerful with the computers now available, from desktops to supercomputers. The Hamilton Jacobi method leads to differential equations which were often impossible to solve in the nineteenth and early twentieth centuries, but which are now easily soluble by computer. It will be interesting to see whether it gives new information about m theory. The aim is to find which combination of methods is the most powerful. For example a combination of Lagrange and Hamilton gives dm(r1) / dr1. The Evans Eckardt equations of motion could be combined with the Hamilton equations or Hamilton Jacobi equations. Your algorithm for the Hamilton equations is new and original, and could well lead to very interesting new results. The Hamilton Jacobi equation for a central potential gives the Schroedinger equation and is a direct route to quantization. The subjects regarded as "complete dynamics" currently include Euler Lagrange, Hamilton and Hamilton Jacobi. However we now have a new complete dynamics, the Evans Eckardt dynamics. The great power of the EE dynamics emerges in m theory. In the Newtonian dynamics and special relativity there are advantages of Euler Lagrange, Hamilton and Hamilton Jacobi, but they are well known. The startling progress has been made with m theory in the year 2018.

Relativistic Hamilton equations

My intention was to write the Hamiltonian directly in a predefined frame of reference by canonical coordiantes without transforming the frame. If frame transformation is required it should be done for the canonical coordinates p_i, q_i directly. The question is if this is possible without knowing the tranformation in a more convenient coordinate set.
However I will try your method below, it is a way to arrive at coordinates in the desired frame. Probably they can then be rewritten to canonical coordinates in that frame.

Horst

Am 29.12.2018 um 15:23 schrieb Myron Evans:

Relativistic Hamilton equations

These results look interesting and can be integrated with Maxima, giving a lot of new techniques. The Hamilton and Hamilton Jacobi equations can be used in any frame of reference. The rule for going from the inertial frame to any other is as follows. In the inertial frame

r double dot = – mMG / r squared

To transform to plane polars use

a bold = (r double dot – r phi dot squared) e sub r
+ (r phi double dot + r phi double dot + r dot phi dot) e sub phi

so we get two equations as in several UFT papers:

r double dot – r phi dot squared = – mMG / r squared

and

dL / dt = 0

The extension to special relativity and m theory is given as you know in UFT415 onwards. . Having used the Hamiltonian method to get the first equation above we know that all is OK. Your previous use of the inertial frame in several papers is also correct. The most powerful equations are our own new equations, dH / dt = 0 and dL / dt = 0. This is because the code can integrate them to give any kind of result.

(r double dot –

relativistic Hamilton equations

Saturday, December 29th, 2018

Relativistic Hamilton equations

These results look interesting and can be integrated with Maxima, giving a lot of new techniques. The Hamilton and Hamilton Jacobi equations can be used in any frame of reference. The rule for going from the inertial frame to any other is as follows. In the inertial frame

r double dot = – mMG / r squared

To transform to plane polars use

a bold = (r double dot – r phi dot squared) e sub r
+ (r phi double dot + r phi double dot + r dot phi dot) e sub phi

so we get two equations as in several UFT papers:

r double dot – r phi dot squared = – mMG / r squared

and

dL / dt = 0

The extension to special relativity and m theory is given as you know in UFT415 onwards. . Having used the Hamiltonian method to get the first equation above we know that all is OK. Your previous use of the inertial frame in several papers is also correct. The most powerful equations are our own new equations, dH / dt = 0 and dL / dt = 0. This is because the code can integrate them to give any kind of result.

(r double dot –

Hamilton.pdf

Note 426(1): New Equations of Motion for m Theory

Friday, December 28th, 2018

Note 426(1): New Equations of Motion for m Theory

The vector method of Eqs. (24), (25), and (37) to (39) is used to define v sub N squared and p and q. as in Eqs. (31) and (36). The vector Hamilton equation p bold dot = – d H / d r bold = – grad H can be used for example, and divides into the equations for p1 and p2. A similar method was used in UFT417 for the lagrangian using the vector Lagrange equations. Eqs. (40) to (46) use the canonically conjugate generalized coordinates p and q in an entirely standard way, but at the same time the discovery is made of the new equation of motion (46) This can now be applied to m theory.
Note 426(1): New Equations of Motion for m Theory

It is not clear to me if you used v_N in the form (26) througout the paper. If so, we are always dealing with two variables q_r and q_phi. The Hamilton and Lagrange equations are defined for q_i and p_i, one cannot build the modulus of q_i for example and use this in the said equations. What do q and p stand for in eqs. (40) ff. ?

Horst

Am 27.12.2018 um 11:09 schrieb Myron Evans:

Note 426(1): New Equations of Motion for m Theory

This notes uses the full power of Euler Lagrange Hamilton dynamics to derive new equations of motion for m theory and for classical dynamics in general. For example the extension of the Evans Eckardt equations in Eqs. (10) and (11) and Eq. (46), a new equation of motion which seems to have been missed hereto. It is tested on the Newtonian and special relativistic levels and found to be correct. These equations can now be applied to m theory, in particular to energy from m space and its spin connection. This energy can become theoretically infinite in m theory. After that, the formalism can be extended to the Hamilton Jacobi level in classical and relativistic physics and also electrodynamics and other subject areas of physics. The relativistic Hamilton Jacobi equation is described in "The Enigmatic Photon" and in the classic books by Landau and Lifshitz.

Note 426(1): New Equations of Motion for m Theory

Thursday, December 27th, 2018

Note 426(1): New Equations of Motion for m Theory

This notes uses the full power of Euler Lagrange Hamilton dynamics to derive new equations of motion for m theory and for classical dynamics in general. For example the extension of the Evans Eckardt equations in Eqs. (10) and (11) and Eq. (46), a new equation of motion which seems to have been missed hereto. It is tested on the Newtonian and special relativistic levels and found to be correct. These equations can now be applied to m theory, in particular to energy from m space and its spin connection. This energy can become theoretically infinite in m theory. After that, the formalism can be extended to the Hamilton Jacobi level in classical and relativistic physics and also electrodynamics and other subject areas of physics. The relativistic Hamilton Jacobi equation is described in "The Enigmatic Photon" and in the classic books by Landau and Lifshitz.

a426thpapernotes1.pdf

FOR POSTING UFT425 Sections 1 and 2 and Background Notes

Thursday, December 27th, 2018

Many thanks again!

FOR POSTING UFT425 Sections 1 and 2 and Background Notes

Posted today

Dave

On 12/26/2018 1:57 AM, Myron Evans wrote:

FOR POSTING UFT425 Sections 1 and 2 and Background Notes

This paper uses the full power of the Euler Lagrange Hamilton dynamics to derive a new equation (30) for the differential function responsible for energy from m space. Section 3 by Horst Eckardt is pencilled in for a computational and graphical analysis of the new Eq. (30) There is a small typo on page 7, Eq. (30) of that page should be Eq. (31). The notes of this paper exemplify Hamiltonian dynamics in detail and are essential reading. The paper is a short synopsis of extensive calculations in the notes, and this is true for all the UFT papers.

FOR POSTING UFT425 Sections 1 and 2 and Background Notes

Wednesday, December 26th, 2018

FOR POSTING UFT425 Sections 1 and 2 and Background Notes

This paper uses the full power of the Euler Lagrange Hamilton dynamics to derive a new equation (30) for the differential function responsible for energy from m space. Section 3 by Horst Eckardt is pencilled in for a computational and graphical analysis of the new Eq. (30) There is a small typo on page 7, Eq. (30) of that page should be Eq. (31). The notes of this paper exemplify Hamiltonian dynamics in detail and are essential reading. The paper is a short synopsis of extensive calculations in the notes, and this is true for all the UFT papers.

a425thpaper.pdf

a425thpapernotes1.pdf

a425thpapernotes2.pdf

a425thpapernotes3.pdf

a425thpapernotes4.pdf

a425thpapernotes5.pdf

Hamiltonian Dynamics in m Theory

Tuesday, December 25th, 2018

Hamiltonian Dynamics in m Theory

Hamiltonian dynamics introduce new information into m theory, via Eq. (26) of Note 425(3). This uses the conjugate generalized coordinates of Hamiltonian dynamics. If the choice (27) and (28) is made we obtain the result (39) which leads to Eq. (44). This is obtained self consistently in two ways, from Eqs. (42) and (43). This analysis leads to Eq. (48), which was the starting point of Note 425(2). The analysis holds in any coordinate system and gives information on dm(r1) / dr1 and m(r1), so they are no longer empirical. In Newtonian dynamics and special relativity this type of analysis does not give new information, but in m theory it gives new information which is just starting to be developed. In Note 425(3) I assumed that partial v1 squared / partial r1 is zero in Eqs. (59) and (60). However Eq. (44) means that partial (m gamma v1 squared) / partial r1 = 0, so the correct result is Eq. (93). This was first derived in Note 425(2) and has been checked by computer algebra. The choice of generalized conjugate coordinates in Eqs. (27) and (28) is the only self consistent choice, and this is by no means obvious. This is one of the things that have to be found by experience or inspection. Note carefully that Lagrangian and Hamiltonian dynamics use generalized coordinates (q dot, q, t) and ( p, q, t) respectively. They are conjugate and independent, so partial q dot / partial q = 0 in Lagrangian dynamics, and partial p / partial q = 0 in Hamiltonian dynamics. The second Hamilton equation (49) of Note 425(3) has not yet been used, and inputs more information. The vector Hamilton equations can also be used. Eq. (93) can be crunched out on a desktop, mainframe or supercomputer, using iterative methods described in a note from Horst yesterday. I checked in Note 425(2) that the Hamilton equations work in special relativity. This is by no means obvious. They also work on the Newtonian level. I first studied these methods as a second year undergraduate in mathematics and wondered why the Euler Lagrange and Hamilton equations were used if they provided the same information as the Newton equations. The answer is that the Euler Lagrange and Hamilton equations use generalized coordinates, and are much more powerful than Newton for this reason. In m theory this is clear, new equations emerge by use of the full range and power of the Euler Lagrange Hamilton dynamics. The Hamilton Principle of Least Action is also very powerful, and the hamiltonian is the basis of quantum mechanics. Anyone who has studied mathematics as an undergraduate should be able to understand what is going on. Those with no experience of mathematics can follow the main arguments and graphics by Horst Eckardt. These are very valuable because they reduce a maze of complicated mathematics to an understandable level.

Fwd: 425(3): Rigorous Self Consistency of m Theory

Sunday, December 23rd, 2018

425(3): Rigorous Self Consistency of m Theory

Many thanks again for these comments, with which I agree. There is an exact self consistency between Eqs. (26) to (28), giving Eq. (47) twice over. Eq. (47) has already been checked by computer so that is one theme of UFT425. Currently I am reading around the basics of hamiltonain dynamics to make sure that there are no errors of concept. This is the first time that hamiltonian dynamics have been used in the UFT series, apart from the derivation of the quantum Hamilton equation in UFT175 and UFT176. In general, the question being asked is what new information is given by the use of hamiltonian dynamics? One example is Eq. (47). As shown in examples worked out by Marion and Thornton, lagrangian and hamiltonian dynamics are used together, so in the next note I will write out these examples to show what I mean, and apply them to orbital theory.

425(3): Rigorous Self Consistency of m Theory
To: Myron Evans <myronevans123>

Thanks, I can follow now the derivation of (36). Concerning eqs. (53-56) for the rest particle, a particle in a Coulomb-like potential cannot be at rest, only for the two return points of the orbit. Are these points meant here? Or a particle fixed by a constraint?
Eqs.(64/65) seem to contain typos. Eq. (57) for the inertial system is

This has two solutions:

I do not find the solutio (67). The Hamiltonian (68) seems simply to be the non-relativistic version of m theory in space (r1, phi).

Eq. (100) leads to
,
a factor of 1/2 seems to be missing. It is to be considered that this m function may be far away from unity for the inertial system, perhaps not very realistic.
Finally I would like to comment that in case of the approximation gamma=const eq. (57) may be solved, giving a transcendent solution. In the case of the inertial system the integration constant can be determined from the condition

m(r1_0) = m_0

Horst

Am 21.12.2018 um 06:20 schrieb Myron Evans:

425(3): Rigorous Self Consistency of m Theory

OK thanks, Eq. (36) was first derived as Eq. (19) of UFT424 and looks OK. Rearrange Eq. (33) as:

gamma squared m(r1) m squared c fourth = p1 squared c squared+ m squared c fourth
and use
E squared = m(r1) squared m squared c fourth gamma squared

to get Eq. (36). To triple check this can be run through the computer.

425(3): Rigorous Self Consistency of m Theory
To: Myron Evans <myronevans123>

I do not understand how (36) is derived from (35) and (33). When rewriting (33) in such a way that the term (35) for E can be inserted, I obtain the result

which depends on gamma. How can I get rid of gamma? Inserting the definition gives an unwanted dependence of v1.

Horst

Am 20.12.2018 um 12:31 schrieb Myron Evans:

425(3): Rigorous Self Consistency of m Theory

This note is a detailed demonstration of the rigorous self consistency of m theory in the elegant Euler Lagrange Hamilton dynamics. This is the first time that detailed consideration has been made of Hamilton’s equations in the UFT series. The self consistent choice of the Hamilton canonical variables is given in Eqs. (27) and (28). This gives the Einstein energy equation (36) in m space, first derived in UFT424. Eq. (47) is obtained in a rigorously self consistent manner from both Eqs. (42) and (43). This checks the starting equation of Note 425(2). The static solution is rigorously equivalent to the rest energy (56) of m theory. The static solution is for a particle m at rest attracted gravitationally by a particle M at rest in m space. The general solution is Eq. (57) and in the inertial frame gives the remarkable result (68) for the hamiltonian, reducing it to classical format in m space. The first Evans Eckart equation reduces this to the force equation in m space in an inertial frame, Eq. (76), giving a new definition of vacuum force, Eq. (80). The hamiltonian can be transformed to plane polar coordinates (r1, phi) giving Eq. (88). Finally the solution obtained in Note 425(2), and checked by computer algebra, is given in Eq. (93) in plane polar coordinates (r1, phi). This related dm(r1) / dr1 to M(r1). This is very complicated equation but can be solved as discussed by Horst this morning. The final note for UFT425 will be considered in the next and final note, using the second Hamilton equation. This is an entirely new classical dynamics valid for any m space.

425(3a).pdf

425(3)-gamma=const.pdf

425(3): Rigorous Self Consistency of m Theory

Friday, December 21st, 2018

425(3): Rigorous Self Consistency of m Theory

OK thanks, Eq. (36) was first derived as Eq. (19) of UFT424 and looks OK. Rearrange Eq. (33) as:

gamma squared m(r1) m squared c fourth = p1 squared c squared+ m squared c fourth
and use
E squared = m(r1) squared m squared c fourth gamma squared

to get Eq. (36). To triple check this can be run through the computer.

425(3): Rigorous Self Consistency of m Theory
To: Myron Evans <myronevans123>

I do not understand how (36) is derived from (35) and (33). When rewriting (33) in such a way that the term (35) for E can be inserted, I obtain the result

which depends on gamma. How can I get rid of gamma? Inserting the definition gives an unwanted dependence of v1.

Horst

Am 20.12.2018 um 12:31 schrieb Myron Evans:

425(3): Rigorous Self Consistency of m Theory

This note is a detailed demonstration of the rigorous self consistency of m theory in the elegant Euler Lagrange Hamilton dynamics. This is the first time that detailed consideration has been made of Hamilton’s equations in the UFT series. The self consistent choice of the Hamilton canonical variables is given in Eqs. (27) and (28). This gives the Einstein energy equation (36) in m space, first derived in UFT424. Eq. (47) is obtained in a rigorously self consistent manner from both Eqs. (42) and (43). This checks the starting equation of Note 425(2). The static solution is rigorously equivalent to the rest energy (56) of m theory. The static solution is for a particle m at rest attracted gravitationally by a particle M at rest in m space. The general solution is Eq. (57) and in the inertial frame gives the remarkable result (68) for the hamiltonian, reducing it to classical format in m space. The first Evans Eckart equation reduces this to the force equation in m space in an inertial frame, Eq. (76), giving a new definition of vacuum force, Eq. (80). The hamiltonian can be transformed to plane polar coordinates (r1, phi) giving Eq. (88). Finally the solution obtained in Note 425(2), and checked by computer algebra, is given in Eq. (93) in plane polar coordinates (r1, phi). This related dm(r1) / dr1 to M(r1). This is very complicated equation but can be solved as discussed by Horst this morning. The final note for UFT425 will be considered in the next and final note, using the second Hamilton equation. This is an entirely new classical dynamics valid for any m space.